Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level

Abstract

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

Multiscale modeling of enzymes: QM‐cluster, QM/MM, and QM/MM/MD: A tutorial review

“…As a recent contribution to advancing the state of the art for electron‐transfer calculations, we mention the work of Blumberger, de la Lande, Elstner, and coworkers who elucidated the distance dependence of electronic coupling for bridge‐mediated charge transfer, for a number of model systems. They used constrained DFT to generate the required diabatic surfaces using both DFT and fragment‐orbital DFT.…”

PyCDFT: A Python package for constrained density functional theory

“…In the past few decades, many research efforts have been dedicated to the development of robust theoretical methods and simulation strategies to describe charge transfer processes in molecules and materials. [ 6–12 ] Charge transfer can take place through a wide spectrum of mechanisms, with two important regimes being the band‐like regime (where transport occurs through delocalized electronic states) and the hopping regime (where transport occurs through localized electronic states). [ 13,14 ] Here, we focus on the hopping transfer, which is the dominant charge transfer mechanism in many organic crystals and conducting polymers and in several metal oxides in the solid state, as well as in many nanoparticle solids.…”

Electronic Couplings for Charge Transfer across Molecule/Metal and Molecule/Semiconductor Interfaces: Performance of the Projector Operator-Based Diabatization Approach

“…There are several different methods to construct diabatic states and calculate the corresponding electronic coupling matrix elements such as block diagonalization, 24,25 generalized Mulliken-Hush method (GMT), 26,27 fragment charge difference, 28 fragment energy difference, 29 projection methods, 30,31 fragment orbital density functional theory (FODFT), [32][33][34][35][36] constrained density functional theory (CDFT) [37][38][39][40] and ultrafast parametrized methods. 41 While the ab initio wavefunction-based approaches are accurate but limited by their high computational cost to small molecules only, the less-demanding DFT methods are typically affected by self-interaction error of uncorrected exchange-correlation functionals.…”